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arXiv · 2605.29231

$\alpha$-stability of Differentially Flat Systems with Application to Newton-Raphson Tracking Control for Vehicle Dynamics

Aadila Ali Sabry·Gennaro Notomista
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Abstract

This paper studies the $\alpha$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $\alpha$-stability, which is particularly amenable to characterize the ability of a system to track dynamic output reference signals. We consider systems controlled using the Newton-Raphson tracking controller, which results in closed-form control policies, therefore it is computationally efficient, and it has been shown to be effective to control a large variety of mobile robots, including autonomous vehicles. The main results of the paper consist in sufficient conditions for the $\alpha$-stability of differentially flat systems and for the equivalence between the proposed control algorithm and the Newton-Raphson tracking controller applied directly to the nonlinear dynamics. We demonstrate the behavior of the proposed controller applied to the kinematic unicycle and dynamic bicycle models.

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Aadila Ali Sabry, Gennaro Notomista. 2026-05-28. $\alpha$-stability of Differentially Flat Systems with Application to Newton-Raphson Tracking Control for Vehicle Dynamics. https://arxiv.org/abs/2605.29231

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